The equation L1 + lambda*L2 = 0 represents the family of all lines passing through the intersection of L1 = 0 and L2 = 0 (for all real values of lambda). This avoids the need to find the intersection point explicitly. Strategy: write the family, apply the additional condition (passes through a point, has a given slope, is tangent to a curve) to find lambda, then substitute back. Note: L2 = 0 itself is also in the family (as lambda approaches infinity).